Journal of Lie Theory 30 (2020), No. 4, 1027--1046
Copyright Heldermann Verlag 2020
Derivations of the Lie Algebra of Strictly Block Upper Triangular Matrices
Prakash Ghimire
Dept. of Mathematics and Physical Sciences, Louisiana State University, Alexandria, U.S.A.
pghimire@lsua.edu
Huajun Huang
Dept. of Mathematics and Statistics, Auburn University, Auburn, U.S.A.
huanghu@auburn.edu
[Abstract-pdf]
\newcommand\Der{\operatorname{Der}} \newcommand\N{\mathcal N} Let $\N$ be the Lie algebra of all $n \times n$ strictly block upper triangular matrices over a field $\mathbb{F}$. Let $\Der(\N)$ be Lie algebra of all derivations of $\N$. In this paper, we describe the elements and the structure of $\Der(\N)$. We also determine the dimensions of component subalgebras of $\Der(\N)$.
Keywords: Derivation, nilpotent Lie algebra, strictly block upper triangular matrix.
MSC: 17B40, 16W25, 15B99, 17B05.
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